Modern Control Engineering

MATLAB Program 7–29 produces the unit-ramp response curves. [Note that the unit-ramp

response is obtained as the unit-step response of C(s)/sR(s).] The resulting curves are shown in

Figure 7–150. The compensated system has a steady-state error equal to one-half that of the orig-

inal uncompensated system.

554 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

Outputs

1.8

0.8

0

1.2

1.6

0.6

0.2

1

1.4

0.4

t Sec

012 3 4 5 6

Unit-Step Responses of Uncompensated System and Compensated System

Uncompensated system

Compensated system

Figure 7–149

Unit-step responses

of the uncompensated

and compensated

systems.

MATLAB Program 7–28

%Unit-step responses

num1 = [10];

den1 = [1 1 10];

num2 = [95.238 286.6759];

den2 = [1 15.3339 110.5719 286.6759];

t = 0:0.01:6;

[c1,x1,t] = step(num1,den1,t);

[c2,x2,t] = step(num2,den2,t);

plot(t,c1,'.',t,c2,'-')

grid;

title('Unit-Step Responses of Uncompensated System and Compensated System')

xlabel('t Sec');

ylabel('Outputs')

text(1.70,1.45,'Uncompensated System')

text(1.1,0.5,'Compensated System')

1/Kv=0.05. The static velocity error constant of the uncompensated system is 10 sec–1. Hence,

the original uncompensated system will have twice as large a steady-state error in following the

unit-ramp input.

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